All eyes will be on the House on Thursday as Speaker John Boehner tries to push through Republicans’ latest proposal to raise the debt ceiling and trim federal deficits. Democratic Senate Majority Leader Harry Reid, who’s keeping his own plan waiting in the wings, has declared Boehner’s plan dead on arrival in his chamber. So, with five days remaining before the government is forced to drastically cut services to avoid a default, Republicans have a bill that can’t pass the Senate, and Democrats have a bill that House Republicans hate. Until that tension is resolved, bipartisan work on a compromise will remain hush-hush. But that doesn’t mean there’s no progress being made.

Reid has reached out to Republican leaders in both chambers to try to find a way to merge Boehner’s bill with his own competing version in the Senate. As Senator Claire McCaskill, a Missouri Democrat, noted on Thursday, the two aren’t so far apart. To close that gap, Democrats are proposing to immediately pass $1.2 trillion in spending cuts along with the debt ceiling hike, followed by the formation of a commission to look for more savings. There are special commissions in both Reid’s and Boehner’s original plans. But here’s the key difference: Dems don’t want another debt ceiling vote to accompany a second round of cuts, as called for in House Republicans’ latest proposal. A compromise would either extend the borrowing limit through 2012 in the first vote or, more likely, President Obama would be given the authority to extend it early next year with only one condition: that Congress have the opportunity to hold a symbolic vote of disapproval. Some Republicans say the changes to Boehner’s bill will be “face saving” “tweaks” but Dems say this is where they will draw the bright line: there will not be another round of debt ceiling brinksmanship before the election.

Meanwhile, the commission would still be working to find $1.8 trillion in further cuts at the behest of Republicans, and Democrats would seek $1 trillion in revenue increases. There are disagreements over what the commission would be empowered to do: Republicans don’t want to touch revenues at all. Without new taxes, Democrats will refuse to cut entitlement benefits from Medicare or Social Security. The bipartisan Senate Gang of Six pushed for a vote on their proposal as a fallback in the event that the commission deadlocks, but House Republicans didn’t like that idea because, naturally, it would include revenue increases. Another idea to instruct relevant House and Senate committees to come up with the cuts through reconciliation — a budget process that has been used as a vehicle for deficit reduction in the past — fell flat because the Senate Finance Committee, the top tax writing organ in the upper chamber, would also surely include revenue increases.

The two sides also are looking for a suitable mechanism that can ensure a second round of cuts will actually happen after the urgency of the debt ceiling hike is gone. The economic ruin that would results from a failure to increase the borrowing limit offers a powerful incentive to push cuts through now. Some similar motivating factor must accompany deficit reduction later on. Without it, talks would likely languish or collapse.

The White House is adamantly opposed to any process that requires raising the debt ceiling a second time before the 2012 election, but they’ve left themselves a sliver of wiggle room. In an official statement of administration policy on Tuesday, Obama’s budget office said that it would recommend a veto of Boehner’s plan for that reason, but the President has declined to make any explicit threat to that end. On Wednesday, White House spokesman Jay Carney repeatedly declined to say that the President would veto a short-term extension, which leaves congressional Democrats some space to negotiate.

Senate Democrats say they now expect Boehner’s unilateral bill to pass the House on Thursday. If happens, they will bring the measure to the Senate floor and kill it. All 53 members of the Democratic caucus have signed a letter stating opposition to Boehner’s plan. Even some Republican Senators, including Lindsey Graham, Rand Paul and Jim DeMint, have come out against the legislation. Once it fails to pass the Senate, the field will be clear for another plan, and House Republican freshmen will be reminded that only a compromise package can pass the upper chamber. Senate Democrats would then offer a new bipartisan agreement, assuming there is one, as a substitute bill.

If all goes as planned — and let’s face it, that’s not something that has happened often in the debt debate — the Senate would then vote to overcome a filibuster on Saturday and pass the bill on Sunday, sending it to the House, where it would face a vote on Monday. Presumably, any bipartisan agreement reached in the Senate would have Democratic support in the House to make up for the group of unyielding Republicans Boehner is sure to lose.

There’s still a very real possibility that congressional leaders will be unable to broker a compromise between their two plans. In that case, Democrats say, the backup plan would be the Reid bill, which is still being tweaked after a Congressional Budget Office analysis released on Wednesday found that it offers $500 billion less in savings than advertised. The deadline is next Tuesday. Skittish markets dipped on Wednesday as they waited for a deal. And one big, terrifying question remains: In this highly charged partisan atmosphere, can Congress actually come up with a solution?